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Chapter 11: Q. 79 (page 774)

The perimeter of a rectangle is 16inches, and its area is 15inches2. What are its dimensions?

Short Answer

Expert verified

The dimensions are 5inchesby3inches.

Step by step solution

01

Step 1. Given information.

Assume the length and breadth of the rectangle is l and b.

From the question,

2l+b=16......(i)l脳b=15......(ii)

Solve equation (ii) for l,

l=15b

Substitute the value of l in equation (i),

role="math" localid="1646842713350" 215b+b=1615+b2b=815+b2-8b=0......(iii)

02

Step 2. Factor equation (iii).

On factoring equation (iii), we get,

b-3b-5=0b=3,5

Substitute b=3in equation (ii),

l脳3=15l=5

Substitute b=5in equation (ii),

l脳5=15l=3

Therefore, the dimension are role="math" localid="1646842885426" 5inchesby3inches.

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