Question

Find x in each of the following



Thanks for helping me btw

Answer 1

The value of x in the given figures from the question, is calculated to be:

g. x = 5

h. x = 4.8

i. x = 5.2

How to calculate for x?

The value of x in the given figures can be calculated as illustrated below:

For question g

• Area of rectangle (A) = 54 cm²
• Length of triangle (L) = x + 4
• Width of triangle (W)= x + 1
• Value of x =?

A = L × W

54 = (x + 4)(x + 1)

54 = x² + x + 4x + 4

54 = x² + 5x + 4

x² + 5x + 4 - 54 = 0

x² + 5x - 50 = 0

x² - 5x + 10x - 50 = 0

x(x - 5) + 10(x - 5) = 0

(x - 5)(x + 10) = 0

x = 5 or -10

Since, measurement is positive, thus, x = 5

For question h

• Area of triangle (A) = 54 cm²
• Height (h) = 8x
• Base (b) = x - 2
• Value of x =?

`A = (1)/(2)bh\\\\54 = (1)/(2)\ * (x\ -\ 2)8x\\\\ 54 = (x\ -\ 2)4x`

54 = 4x² - 8x

4x² - 8x - 54 = 0

olving by formula method, we have:

• a = 4
• b = -8
• c = -54

`x = (-b\ \pm\ √(b^2\ -\ 4ac))/(2a) \\\\x = (-(-8)\ \pm\ √((-8)^2\ -\ (4\ *\ 4\ *\ -54)))/(2\ *\ 4)\\\\x = (8\ \pm\ √(64\ +\ 864))/(8)\\\\x = (8\ \pm\ √(928))/(8)\\\\x = (8\ +\ √(928))/(8)\ or\ (8\ -\ √(928))/(8)\\\\x = 4.8\ or\ -2.8`

Since measurement is positive, thus, x = 4.8

For question i

• Area of rectangle (A) = 54 cm²
• Length of triangle (L) = 2x
• Width of triangle (W)= x
• Value of x =?

A = L × W

54 = 2x(x)

54 = 2x²

27 = x²

`√(27) = x`

x = 5.2

Answer 2

a). The value of x for the Isosceles triangle is equal to 2

b). The value of x for the rectangle is equal to 2½

c). The measure of c for the angles on the straight line is 50°.

How to evaluate for the unknown values.

a). The figure is an Isosceles triangle which implies its two sides are equal so given the perimeter of 28cm we have that;

8 + 2(4x + 2) = 28

8 + 8x + 4 = 28 {open bracket}

12 + 8x = 28

8x = 28 - 12 {collect like terms}

8x = 16

x = 16/8 {divide through by 8}

x = 2

b). The rectangle has the length of its opposite side to be equal, so we solve for x as follows:

4x + 2 = 2x + 7

4x - 2x = 7 - 2 {collect like terms}

2x = 5

x = 5/2

x = 2½

c). The sum of angles on a straight line is equal to 180°, thus the measure of c is calculated as follows:

c + c + 80 = 180

2c + 80 = 180

2c = 180 - 80 {collect like terms}

2c = 100

c = 100/2 {divide through by 2}

c = 50

In conclusion, tge value of x for the Isosceles triangle is 2, the value of x for the rectangle is equal to 2½ and the measure of c for the angles on the straight line is 50°.