Still preparing for a test tomorrow. We have not even even done any of these problems before?

Question

The length of one leg of a right triangle is 3/4 of the length of the other leg. If the length of the hypotenuse is 15 inches, find the area of such triangle. How do I set up this problem?

Answer 1

a = 15
b = 3/4c
c = ?
a² = b² + c²
15² = (3/4c)² + c²
225 = 9/16c² + c²
GCF(1, 16) = 16
3600 = 9c² + 16c²
25c² = 3600
c² = 3600 : 25
c² = 144
c = \/144 = 12
a = 15; b = 3/4c = 9; c = 12.

A = (b*h) : 2
A = (12 x 9) : 2
A = 54 in²
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Answer 2

The area of a triangle is 1/2(base * height). Since your triangle is a right triangle this makes the base and height numbers equal to the 2 legs of the triangle that are not the hypotenuse. (The two legs that are joined by the 90 degree angle that is)

The hypotenuse of a triangle can be used as well. Since one leg squared times the other leg squared is equal to the hypotenuse squared. Or a^2 + b^2 = c^2, where a and b are the sides of the triangle and c is the hypotenuse, this is also known as the Pythagorean theorem.

Use, 1/2(a*b), where you can substitute a=3/4b. And use a^2 +b^2 = (15)^2. You can also substitute a=3/4b here as well to help you.

Answer 3

I can help u :) it's called "Pythagoras theorem" it says that:
-we note hypotenuse with x
-we note one of the leg with l1 and the other one with l2
-and the theorem says: x*x=l1*l1+l2*l2
but I'll make it a bit easier to you and I'll adapted to your case:
so you say that leg1 is 3/4 of leg2 but there is a theory that states that the hypotenuse 5/5 leg2 is 4/5 an leg1 is 3/5

so you divide 15 trough 5 and you get 3,so that means that 5*3=15,but leg one is only 4/5 of the hypotenuse so you only take 4*3=12=leg2 and leg one only need 3*3=9

so as Pythagoras says 15*15=12*12+9*9
225=1424+81
and to calculate the area you need to do (leg1*leg2)/2

so: leg1=9
leg2=12

(9*12)/2=108/2=54 so the area of your triangle is 54


I HOPE YOU UNDERSTAND HOW I'VE CALCULATED ALL THIS :) good luck for the test tomorrow

Answer 4

in a right triangle a^2 + b^2 = h^2
where a and b are sides and h is hypotenuse

and we know that a = 3/4b

replacing we get
(3/4b)^2 + b^2 = 15^2
9/16 b^2 + b^2 = 225
25/16 b^2 = 225
b^2 = 144 => b= 12
and a = 3/4 * 12 = 9

Answer 5

use the Pythagorean theorem:

make one leg x and the other leg 3/4x because you know it is 3/4 of the other leg

(3/4x)^2 + x^2 = (15)^2

sove for x and you get

x=12

take 3/4x to find the other side
3/4(12) = 9

then use the formula for the area of a right triangle 1/2 base x height

(12 x 9)/2 = 108/2 = 54

Answer 6

Remember that a^2 + b^2 = c^2

c = hypotenuse (15)
and b is 3/4a or 0.75a

so a^2 + (0.75a)^2 = 15^2

a^2 +0.5625(a^2)=225
1.5625(a^2) = 225

divide both sides by 1.5625

a^2 = 144
square root of 144 = 12

so a=12

b is 0.75a
b=9

a=12, b=9, c=15

Answer 7

Let L1 be one leg,

then the other leg is L2 = 3L1/4

and you know Pythagora's theorme

L1^2 + L2^2 = D^2, where D is the diagonal, or hypothenuse = 15

so, substitute for L2 and you have one equation in one unknown, L1, solve for L1, then get L2.

Use the equation for the area of a right triangle.

Answer 8

x² + (3x/4)² = 15²
x² + 9x²/16 = 225
16x² + 9x² = 3600
25x² = 3600
x² = 144

x = 12

=>
3(12)/4 = 9

Area:
A = 9*12/2 = 54 in²

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