Question

the height of triangle pqr is double the hight of triangle abc, while tye base of tirange abc is double the base of triangle pqr the ratio of th areas of triangles abc and par will be. (a) 1:1 (b) 1:2 (c) 2:1 (d) 2:3​

Answer 1

Answer:

The ratio of the areans of the 2 triangles is (b) 1:1. (I suppose)

Step-by-step explanation:

(How i figured)

As h1 = 2xh2 and b1 = 1/2xb2

1/2b1h1 over 1/2b2h2

=  1/2xb2x2h2 over b2xh2

= b2h2 over b2h2

as 1/2 and 2 cancel out each other

Answer 2

Answer :

The correct answer is option A

The ratio of area of ∆ ABC to area of ∆ PQR is 1:1

Step-by-step Explanation :

Let the Height and base of triangle PQR be H1 & B1

And height and base of triangle ABC be H2 and B2

So According to given conditions,

H1 = 2(H2) ------------. (1)

B2 = 2(B1) --------------- (2)

To find : Area of ∆ ABC : Area of ∆ PQR

We know that,

Area of triangle = 1/2 × base × height

So, substituting the given value in above formula we get,

Area of ∆ABC = 1/2 × B1 × H1

substituting H1 = 2H2 in above equation,

Area of ∆ABC = 1/2 × B1 × 2(H2)

Area of ∆ ABC = B1 × H2 ---------(3)

Also,

Area of ∆ PQR = 1/2 × B2 × H2

Substituting B2 = 2(B1) in above equation we get,

Area of ∆ PQR = 1/2 × 2(B1) × H2

Area of ∆ PQR = B1 × H2 ------------(4)

Dividing equation (3) by (4) we get

Area of ∆ ABC/ Area of ∆ PQR = 1/1