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JAMB Mathematics 2023 Paper

Question : 60

Total: 80

^2

Solution:

Let the length of the longer side = $x$ cm

∴ The length of the shorter side = (

x

- 6) cm

If we increase each side's length by 2 cm, it becomes

(

x

+ 2) cm and (

x

- 4) cm respectively

Area of a rectangle = L x B

A_1 = x(x - 6) = x^2 - 6x

A_2 = (x + 2)(x - 4) = x^2 - 4x + 2x - 8 = x^2 - 2x - 8

A_1 + 68 = A_2

(Given)

⇒

x^2 - 6x + 68 = x^2 - 2x - 8

⇒

x^2 - x^2 - 6x + 2x

= -8 - 68

⇒ -4

x

= -76

⇒ $\frac{-76}{-4}$ = $x$ = 19cm

∴ The length of the shorter side = $x$ - 6 = 19 - 6 = 13 cm

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