find the area of a right triangle whose legs have lenghts wich differ by 7m and whose hypotenuse is 17m long.?

Question

please show complete solution

Answer 1

15^2 + 8^2 = 17^2
A = bh/2 = [15 * 8 / 2] m^2 = 60 m^2

Answer 2

let hyp = c, other sides a and b
we know a^2+b^2=17^2
b=a+7
a^2+(a+7)^2=289
a^2+a^2+14a+49=289
Collect like terms and rearrange
2a^2+14a-240=0

Factorise
a^2+7a-120=0
(a-8)(a+15) = 0

a = 8 or a = -15 by null factor law. A can't be negative so a = 8.
b = a+7 = 15

Double check 15^2+8^2 = 289 = 17^2 so it's correct.
Area of triangle = base x height/2 or in this case a x b/2
Area = 15*8/2 = 120/2 = 60 meters squared

Answer 3

x and x+7 are the legs and the hyp =17.So Pythagoras
x^2+(x+7)^2 = 17^2
2x^2 +14x +49 = 289==> x^2 +7x -120 =0 Applying formula for 2nd degre equ. and taking the `positive solution x=8 the other leg is 15 and the area is 8*15/2 = 60 sq.m

Answer 4

ideal triangles are the common ones. because it truly is a ideal triangle, imagine about once you've 2 of them to make a rectangle. you recognize the portion of a rectangle is length x width. save in recommendations how the right triangle is 0.5 is that rectangle? So (length x width)/2. So on your difficulty: (6 x 8)/2. (40 8)/2. 24. and remember to label! 24 instruments^2. (Or 24 sq. instruments).

Answer 5

If a and b are the two sides, a > b

a^2+b^2 = 17^2

(a^2+b^2) = (a -b)^2 + 2ab.

2ab = (a^2+b^2)-(a -b)^2

2ab =17^2 - 7^2 = 240.

ab = 120 .

Area = ab/ 2 = 60 sq m

Answer 6

let the first leg = L1
let the second leg = L2
L1 - L2 = 7............... equation (*)
square of (hypotenuse) = 289
square of (hypotenuse) = square of L1 + square of L2
square of L1 + square of L2 = 289.............. equation (1)
L1 - L2 = 7 (by squaring)
square of L1 - square of L2 = 49................. equation (2)

by adding equation (2) to equation (1):
square of L1 + square of L2 = 289
+
square of L1 - square of L2 = 49
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2 square of L1 = 338 (dividing by 2)
square of L1 = 169 (by talking square root)
L1 = 13 cm
by substituting in equation(*)
L1 - L2 = 7
13 - L2 = 7
- L2 = 7 - 13
- L2 = - 6
L2 = 6 cm
area of the triangle = 1/2 * base * height
area of the triangle = 1/2 * 13 * 6
area of the triangle = 39 cm square