Question

Ratio of areas of two triangles with equal heights is 2:3 . If base of the smaller triangle is 6 cm then what is the corresponding base of the bigger triangle​

Answer 1

Answer:

$\underline{\purple{\ddot{\Mathsdude}}}$

♧♧Answered by Rohith kumar maths dude :-

♧♧Given: -

• Ratios of areas of two triangles with equal heights is 2:3.

♧♧To prove:-

• corresponding base of bigger triangle

♧♧Proof:-

♧Let M1 and M2 be the areas of two triangles .

♧And N1 and N2 be their corresponding bases.

M:M= 2:3

♧♧Therefore,

M1/ M2 = 2/3

• M1/M2=N1/N2 (are have equal heights )

2/3=6/N2

b2= (6×3)/2

b2=9cm.

♧♧Hence, the corresponding sides of bigger triangle is 9cm.

♧♧Hope it helps u mate .

♧♧Thank you .

Answer 2

Answer:

Let us assumed that,

Area of bigger triangle = $\sf \: A_1 = \frac{1}{2} \times h \times BC$

Area of smaller triangle = $\sf \: A_2 = \frac{1}{2} \times h \times EF$

Base of smaller triangle = EF = 6 cm

Base of bigger triangle = BC = to find

So according to the question,

Given,

$\: \: \: \: \: \: \: \: \: \sf \: A_1 : A_2 = 2 :3 \\ \implies\sf \: \frac{A_1}{A_2} = \frac{2}{3} \: \: \: \: \\\implies\sf \: \frac{\frac{1}{2} \times h \times BC}{ \frac{1}{2} \times h \times EF} = \frac{2}{3} \\ \implies\sf \: \frac{BC}{EF} = \frac{2}{3} \\ \implies\sf \: \frac{BC}{6} = \frac{2}{3} \\ \implies\sf \:BC = \frac{2 \times 6}{3} \\ \implies\sf \:BC = 4 \: cm$

So base of bigger triangle BC = 4 cm