1)A rectangle has a diagonal of 10 and length of 8. Find its width.
My answer is 6? correct?
2) The legs of an isosceles triangle are 13 units long and the altitude to the base is 12 units long. Find the length of the base.
My answer is 10? Correct?
If I'm wrong please explain to me how to do it. Thanks!
2007-08-24 14:19:14 · 10 answers · asked by Randy M 1 in Science & Mathematics ➔ Mathematics
You are right, both are right
2007-08-24 14:25:36 · answer #1 · answered by Mugwump 7 · 1⤊ 2⤋
Brilliantly done mate. Keep up the good work.
As a short-cut to the pythagorean thyrum which is no doubt what you're working on here. The triangle described in the first question I could find the answer in my head instantly. And no, I cannot square and square root things in my head, but I wish. That particular triangle is a "special triangle". That one specifically is the "3-4-5" triangle refering to lengths of the sides. Since the hypotonuse of the triangle is 10 (5*2) and one leg is 8 (4*2) then it must be a "3-4-5" triangle, therefore the other leg is clearly 6 (3*2) but if you don't get that don't confuse yourself. =]
2007-08-24 14:32:31 · answer #2 · answered by notallchipsarefood 3 · 0⤊ 0⤋
Both of your answers are correct. The reason why some believe the second is wrong is because to solve it you would have to take out half of the isosceles triangle and make another triangle and find its base using the other two measurements given. But that base is only half of the whole original triangle's base. So you were correct on doubling it. Good job.
2007-08-24 14:34:25 · answer #3 · answered by Anonymous · 0⤊ 0⤋
L = W + 6 : (The length of a fenced rectangular garden is 6 feet longer than the width) 2L + 2W = 80 (. If the length of the fence used to surround the garden is 80 feet) so you have two equations L = W + 6 2L + 2W = 80 substitute the first one into the second one gives : 2(W+6) + 2W = 80 2W + 12 + 2W = 80 4W = 80 - 12 W = 20 - 3 = 17 W = 17 since W = 17 and L = W + 6 , it follows that L = 17 + 6 = 23 the other one goes the same : G = T - 3 (Grace is 3 years younger than Tanya) (G-2) + (T-2) = 41 (Two years ago the sum of their ages was 41) again substitute G = T-3 into the other equations and bingo
2016-05-17 07:44:04 · answer #4 · answered by ? 3 · 0⤊ 0⤋
Both your answers are correct. Dont forget the pythag. theorem, a^2+b^2=c^2.
1) Excellent! This is a 3-4-5 triangle (6-8-10)
2) Good job. You remembered to double 5 to get your entire base.
2007-08-24 14:33:32 · answer #5 · answered by Grace 2 · 0⤊ 0⤋
a^^2 + b^^2 = c ^^2
64 + 36 = 100
sqrt ( 36 ) = 6
your first is correct
question 2
1/2 the base makes a right triangle with base of 6
144 + 25 = 169
sqrt(25) = 5
5 * 2 = 10
your second answer is correct
2007-08-24 14:27:35 · answer #6 · answered by zenmaster55555 2 · 2⤊ 0⤋
1) Yes. The square of the hypotenuse is equal to the sum of the square of each side (pythagorus theorum), i.e.:
hypotenuse^2 = length^2 + width^2
width^2 = hypotenuse^2 - length^2
width = (hypotenuse^2 - length^2) ^ 0.5
= (10^2 - 8^2)^ 0.5
= 6
2) Yep, same math applies:
width = (hypotenuse^2 - length^2) ^ 0.5
= (13^2 - 12^2)^ 0.5
= 5, which you then double to get the full length of the base
2007-08-24 14:27:32 · answer #7 · answered by Mark F 6 · 1⤊ 0⤋
I know the first one is correct, but I'm not sure about the second.
2007-08-24 14:24:21 · answer #8 · answered by Confusion 2 · 0⤊ 0⤋
Both your answers are correct
2007-08-24 14:25:16 · answer #9 · answered by crystalline.angel 2 · 2⤊ 0⤋
your first answer is correct
but ur 2nd answer is incorrect it shoukd be 5
(13)^2=(12)^2+x^2
x^2=169-144
x^2=5^2................==25
x=5
2007-08-24 14:25:11 · answer #10 · answered by saurav 2 · 0⤊ 3⤋