Question

A lawn is in the shape of a right angled triangle. the lengths of the 2 shorter sides are

(x+2) meters and (4x+4) meters while the length of the hypotenuse is (5x) meters. form and solve an equation in x and find the area of the lawn in metres squared

Answer 1

x = 5 m

Area = 84 m^2

Explanation:

Since we have a right triangle, we can use the Pythagorean Theorem to solve for the unknown, which is the hypotenuse, since it will have the longest side.

x^2 + y^2 = z^2, where z is the hypotenuse.

(x+2)^2 + (4x+4)^2 = (5x)^2

(x^2 + 4x + 4) + (16x^2 + 32x + 16) = 25x^2

17x^2 + 36x + 20 = 25x^2

-8x^2 + 36x + 20 = 0

-4(2x^2 - 9x -5) = 0

-4(x - 5)(2x + 1) = 0

x = 5 and x = -(1/2)

x = 5 is the choice since -(1/2) would mean a negative length,

The area is (1/2)(base)(height)

(1/2)(x+2)(4x+4)

(1/2)(5+2)(4*5+4) Use x = 5

(1/2)(7)(24)

Area = 84 m^2