Question

13. The width of a rectangular hall of Ruiri Girls Secondary School is 16m less than its length. Calculate the length of the hall if its area is 132m². Hence calculate its perimeter. (4 mks)​

Answer 1

length = 16 m , perimeter = 56 m

Explanation:

let l be length then width = l - 16

area (A) is calculated as

A = length × width

= l(l - 16)

given A = 132 , then

l(l - 16) = 132

l² - 16l = 132 ( subtract 132 from both sides )

l² - 16l - 132 = 0 ← quadratic in standard form

(l - 22)(l + 6) = 0 ← in factored form

equate each factor to zero and solve for l

l - 22 = 0 ⇒ l = 22

l + 6 = 0 ⇒ l = - 6

however, l > 0 , then l = 22 and w = l - 16 = 22 - 16 = 6

the length of the hall is 22 m , width is 6 m

the perimeter (P) of a rectangle is calculated as

P = 2 (length + width)

= 2(22 + 6)

= 2 × 28

= 56 m