Question

A rectangles base is 9cm longer than its height . The rectangles area is 162cmsq. Find it’s height and base.

Answer 1

First of all remember to use correct subject for questions.
This question belong to maths


Anyway, your answer :-


Given that base is 9 cm longer than height

Let height be x

then base = 9 + x

Given that area = 162 cm²

We know that area of rectangle
= length × breadth
= base × height


So, base × height = area

=> (9 + x)(x) = 162

=> 9x + x² = 162

=> x² + 9x - 162 = 0

=> x² + 18x - 9x - 162 = 0

(by splitting the middle term method)

=> x(x + 18) - 9(x + 18) = 0

=> (x + 18)(x - 9) = 0

=> (x + 18) = 0/(x - 9)

=> (x + 18) = 0

=> x = - 18

or,

(x - 9) = 0/(x + 18)

=> x - 9 = 0

=> x = 9

But dimensions can't be negative
Hence, x ≠ - 18

So, x = 9

=> Base = 9 + x

=> Base = 9 + 9 = 18


Hence,

Height = 9
Base = 18