English Medium Class 9 - CBSE Question Bank Solutions

Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and the two parallels.

A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of ₹ 5000 per m² per year. A company hired one of its walls for 3 months. How much rent did it pay?

There is a slide in the park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see the given figure). If the sides of the wall are 15m, 11m, and 6m, find the area painted in colour.

Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.

Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.

An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:

`f ( x ) = 3x +1, x = - 1/3`

Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:

`f(x)=x^2- 1,x=1,-1`

In Fig. 10.22, the sides BA and CA have been produced such that: BA = AD and CA = AE.
Prove that segment DE || BC. 

In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that: LN = MN. 

Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:

`g(x)=3x^2-2,`  `x=2/sqrt3     2/sqrt3`

In a ΔABC, if AB = AC and ∠B = 70°, find ∠A. 

Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:

`f ( x ) = 5x - pi , x = 4/5`

Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:

`f ( x) = x^2and x = 0`

Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:

`f(x) = lx + m , x = - m/1`

Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:

`f (x) = 2x +1, x = 1/2`

BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.  

In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the othe Prove that the triangles are congruent.

If `x = −1/2` is a zero of the polynomial `p(x)=8x^3-ax^2 -+2` find the value of a.