Question

1. A number is 12 more than the other. Find the numbers if their sum is 48.
2. A 300 m long wire is used to fence a rectangular plot whose length is twice its width. Find the length and breadth of the plot
3. The length of a rectangle is 10 m more than its breadth. If the perimeter of rectangle is 80 m, find the dimensions of the rectangle.
4. Among the two supplementary angles, the measure of the larger angle is 36° more than the measure of smaller. Find their measures.
5. The length of a rectangle is three times its width. It the perimeter of the rectangle is 96m, find the length and breadth of the rectangle.

Answer 1

Answer:

Answer (1)

Given :-

• A number is 12 more than other.
• Sum of numbers = 48

To Find :-

Both numbers

Solution :-

Let the smaller number be x

$\sf \: x + x + 12 = 48$

$\sf \: 2x + 12 = 48$

$\sf 2x = 48 - 12$

$\sf \: 2x = 36$

$\sf \: x = \dfrac{36}{2}$

$\sf \: x = 18$

$\sf \: x + 12 = 18 + 12 = 30$

The numbers are

12 and 30

Answer (2)

Given :-

• Length of wire = 300 m
• Length is twice of breadth

To Find :-

Length and breadth

Solution :-

When we fence anything we find its perimeter.

The perimeter of plot = Length of wire

Now,

Let the breadth be x

Length = 2 × x = 2x

$\sf \: 300 = 2(2x + x)$

$\sf \: 300 = 4x + 2x$

$\sf \: 300 = 6x$

$\sf \: x = \dfrac{300}{6}$

$\sf \: x = 50$

$\sf \: 2x = 2(50) = 100$

The length of rectangle is 100 m and breadth is 50 m.

Answer (3)

Given :-

• Length is 10 m more than its breadth
• Perimeter = 80 m

To Find :-

The length and breadth

Solution :-

Let the breadth be y and Length = y + 10

$\sf \: 80 = 2(y + 10 + y)$

$\sf \: 80 = 2y + 20 + 2y$

$\sf \: 80 = 4y + 20$

$\sf \: 80 - 20 = 4y$

$\sf \: 60 = 4y$

$\sf \: y = \dfrac{60}{4}$

$\sf \: y = 15$

$\sf \: y + 10 = 15 + 10 = 25 \: m$

Therefore

Length of rectangle is 25 m and breadth is 15 m.

Answer 4 :-

• There are two supplementary angle
• One is 36⁰ more than another

To Find :-

Both angle

Solution :-

Let the smaller angle be x

As we know that sum of supplementary angle is 180⁰

$\sf \: x + x + 36 = 180$

$\sf \: 2x + 36 = 180$

$\sf \: 2x = 180 - 36$

$\sf \: 2x = 144$

$\sf \: x = \dfrac{144}{2}$

$\sf \: x = 72$

$\sf \: x + 36 = 72 + 36 = 108$

The two angles are 72 and 108⁰.

Answer (5)

Given :-

• Length is thrice of its width
• Perimeter = 96 m

To Find :-

Length and width

Solution :-

Le the breadth be x and length be 3x

$\sf \: 96 = 2(3x + x)$

$\sf \: 96 = 6x + 2x$

$\sf \: 96 = 8x$

$\sf \: x \: = \dfrac{96}{8}$

$\sf \: x = 12$

$\sf \: 3x = 3(12) = 36$

Therefore

Length of rectangle is 36 m and breadth is 12 m.

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