Question

The area of a rectangular room is expressed as $10s–15t+40$. Which of the following expressions represents its dimensions?
Hint: Area of a rectangle $=\text{Length}\times \text{Width}$

• A. $5\text{and}(2s–3t+8)$
• B. $10\text{and}(2s–3t+4)$
• C. $5\text{and}(2s+3t+8)$
• D. $2\text{and}(5s–3t+20)$

Answer 1

The correct option is A $5\text{and}(2s–3t+8)$

If the area of the room is given, we can determine the dimensions of the room by factorizing the expression for the area.
The terms in the expressions are $10s,15t,\text{and}40$.
First, find the HCF of $10s,15t,\text{and}40$ by writing their prime factors.
$10s=2\times 5\times s$
$15t=3\times 5\times t$
$40=2\times 2\times 2\times 5$
HCF of $10s,15t,\text{and}40=5$
Now, if we write the expression using its HCF,
$10s–15t+40=5\times 2s–5\times 3t+5\times 8=5\times (2s–3t+8)$
The factors of $10s–15t+40\text{are}5\text{and}(2s–3t+8)$.
So, the dimensions of the room are 5 and $(2s–3t+8)$.