Question

if the length of a triangle is halved and it's breadth is tripled what is the percentage change in it's area?​

Answer 1

$\frac{1}{2}$${\large{\underbrace{\underline{\bf{Question:-}}}}}$

If the length of a triangle is halved and it's breadth is tripled what is the percentage change in it's area?​

${\large{\underbrace{\underline{\bf{Answer:-}}}}}$

Let original length be = x

Let original breadth be = y

Area of triangle = $\frac{1}{2}$ × bh

Area of original triangle =   $\frac{1}{2}$ × xy

                                       = $\frac{xy}{2}$

According to question,

New length =   $\frac{x}{2}$

New breadth = 3y

New area of traingle = $\frac{1}{2}$  × $\frac{x}{2}$  × 3y

                                   = $\frac{3x}{4}$

∴ Percentage increase in the area of the original and the new triangle =

$\frac{ΔA}{A}$  × 100%

=  $\frac{1}{2}$ × bh × 2

= bh × 100

= 50%

∴, there is 50% increase in the area of triangle.

✭ NOTE -

To solve these kinds of questions, one has to first find the area of the given figure then according to the conditions stated in the question, you are advised to find the area of new figure. Divide the values and you'll get your answer!

Hope this helps uh! ♡

Answer 2

Answer:

• Let original length be = x

• Let original breadth be = y

Area of triangle = 1/2 × bh

Area of original triangle = 1 /2 × xy = 2/xy

According to question,

New length = x/2

New breadth = 3y

New area of traingle.

= 1/2× x/2 × 3y

= 3x-4

∴ Percentage increase in the area of the original and the new triangle =ΔA/A × 100%

= 1/2 × bh × 2

= bh × 100

= 50% Ans.