Question

the rectangle shown has a perimeter of 40cm and the given area of 64 cm squared it's length is 8 more than twice its width write and solve a system of equations to find the dimension of the rectangle

Answer 1

16 = l

4 = w

Explanation:

{64 = wl

{40 = 2w + 2l

{l = 8 + 2w

64 = w[8 + 2w] ↷

-64 + 8w + 2w² ↷

[2w² - 8w] + [16w - 64]

2w[w - 4] 16[w - 4]

[w - 4][2w + 16] = 0

↑

This is the expression we want because when we talk about dimensions, we want NON-NEGATIVE numbers. The other expression results in -8 = w, and we do not want that; this expression gives us a solution of 4 = w, and THIS is exactly what we want. Anyway, you plug "4" back into the system of equations and you will get a length of 16 centimetres.

I am joyous to assist you anytime.