Question

Look at image!!! Math questions,urgent!!!

Answer 1

1: c. 31 feet

2: a. Width: 44 inches
Height: 33 inches

Explanation:

Question 1

For a rectangle with each angle = 90° , the diagonal can be determined by the Pythagorean theorem

`D = \sqrt{L^(2) + W^2\\\\`

where L = length and W = width

Taking 30 to be the length and 9 the width, the diagonal length so that all angles are 90° should be

`D = √(30^2+9^2)\\\\D = √(900 + 81)\\\\D = √(981)\\\\D = 31.32\\`

which when rounded to the nearest foot is 31

Answer to 1 is c. 31 feet

Question 2
The aspect ratio is defined as

`(Width(W))/(Height(H))`
Here aspect ratio =
`(4)/(3)`

so
`(W)/(H) = (4)/(3)`

or
`H = (3)/(4)W`

A 55" television will have its diagonal as 55 inches

`\text{Diagonal D = } \sqrt{W^2 + H^2\\\\`

`D^2 = H^2 + W^2\\\\\\\text{since } H = (3)/(4)W\\\\D^2 = W^2 + ((3)/(4)W)^2\\\\D^2 = W^2 + (9)/(16)W^2\\\\\\D^2 = W^2(1 + (9)/(16))\\\\D^2 = W^2 \cdot (25)/(16)\\\\D^2 = (25)/(16)W^2\\\\D = \sqrt{(25)/(16)} W`

==>

`D = (5)/(4) \cdot W`

But we know that D = 55

So we get

`55 = (5)/(4) W\\\\W = (4)/(5) \cdot 55\\\\W = 44`

Since

`H = (3)/(4) W\\\\H = (3)/(4) 44\\\\H = 33\\`