Question

Q 1) The base and height of a triangle are in the ratio 3:4 and it's area is 96cmsquare.Find it's base and height.
Q2) A rectangular field is 24m long and 15m wide. How many triangular flower beds each of base 3m and altitude 4m can be laid in this field?

Answer 1

1. ATQ, the base and height of the triangle are in ratio 3 : 4

let the base and height of the triangle be 3x and 4x Respectively.

area of the triangle = 96cm²

therefore 1/2 × b × h = 96cm²

==> 1/2 × 3x × 4x = 96cm²

==> 12x² = 96/2

==> 12x² = 48

==> x² = 48/12

==> x² = 4

==> x = √4

==> x = 2

hence, base of the triangle = 3x = 3 × 2 = 6cm and height of the triangle = 4x = 4 × 2 = 8cm.

2. given the length of the rectangular field = 24m and breadth of the rectangular field = 15m.

area of the rectangular field = l × b

= 24 × 15

= 360m²

area of the triangular flower bed = 1/2 × b × h

= 1/2 × 3 × 4

= 3 × 2

= 6m²

hence, no. of flower beds can be laid in the field = 360/6 = 60 flower beds

HOPE THIS HELPS..!!

Answer 2

a1)let the base and height be 3x and 4 x
so area is 1/2 ×3x×4x=96
3x×2x=96
6x^2=96
x^2=96/6
x^2=16
=>x=4
base is 3x=3×4=12
height is 4x=4×4=16


a2)
area of field =l×b=24×15=360m^2
area of each triangular bed 1/2×3×4=6m^2
triangular beds that can be laid ois
360/6
=60
therefore 60 such triangular beds can be laid