Question

1. Melisa had some stickers and game cards in the ratio 5:8. she has 96 game cards. how many stickers did she have ?

2. The base and the height of triangle ABC are in the ratio 3:2. the base of triangle is 96 cm.
find the hight of triangle and the area of triangle

thank you very much​

Answer 1

Given 1 :-

Here ,

Melisa had Some stickers and game cards in the ratio 5 : 8

The number of game cards are 96

Solution 1 :-

Ratio of stickers and game cards = 5:8

Let the ratios be 5x and 8x

The no.of game cards = 96

Therefore ,

8x = 96

x = 96 / 8

x = 12

Thus , The no.of stickers are 5x = 5 * 12 = 60.

Hence , The number of game cards are 96

The number of stickers are 60 .

Given 2 :-

The base and the height of triangle ABC are in the ratio 3 : 2

The base of the triangle is 96 cm

Solution 2 : -

Ratio of base and height = 3 : 2

Let the ratios be 3x and 2x

The base of ΔABC is 96cm

Therefore ,

3x = 96

x = 96/3

x = 32

Thus the height of the triangle ABC

= 2 * 32cm = 64cm

Hence , The base of ΔABC is 96cm

The height of ΔABC = 64cm

Now ,

The Area of triangle = 1/2 * Base * height

Put the required values ,

Area of ΔABC = 1/2 * 96 * 64

Area of ΔABC = 48 * 64

Area of ΔABC = 3072 cm^2 $.$

Answer 2

Question 1)

Given:-

Ratio of stickers to game cards=5:8

No of cards=96

To find:-

The number of stickers.

Solution:-

Let us consider the number of stickers as 5x and game cards as 8x.

8x=96

x=12

so,

No of stickers=5 * x

=5*12

=60

Therefore, the number of stickers is 60.

                                                                             

Question 2)

Given:-

Base of the triangle ABC to height of the triangle=3:2

Base of the triangle = 96 cm

To find:-

The height of triangle.

Solution:-

Let us consider the base as 3y and height as 2y

3y=96

y=32cm

so,

Height of triangle=2y

=2*y

=2*32

=64cm

Therefore, the height is 64 cm

Area of the triangle=1/2 *base*height

=1/2+96*64

=3072 cm²