. The rectangle has a perimeter of 28 cm and a diagonal length of 10 cm. Determine the dimensions of the rectangle.

length = 8cm; width = 6cm

Step-by-step explanation:

The dimensions of a rectangle are the length and width:

Let x be the length of rectangle, and

y, the width of rectangle

Perimeter equals 2x+2y=28, divide through by 2: x+y=14

Make y the subject, y=14-x, input the value of y into the equation and solve by pythagorean theorem:

x^2 + y^2= 10^2 = 100

x^2 + (14-x)^2 =100

x^2 +196-28x + x^2= 100

2x^2- 28x +196= 100

2x^2 -28x +96 =0

x^2 -14x + 48= 0

(x- 8) (x- 6)= 0

x= 8; or x = 6

The length of rectangle is 8 cm

The width of rectangle is 6 cm

I hope this helps.

Good morning ☕️

Length = 8 cm

width = 6 cm

Step-by-step explanation:

consider L the length of the rectangle and w its width.

Statement 1 : The rectangle has a perimeter of 28

means  L + w = 14

statement 2 : the rectangle has a diagonal length of 10

means  10² = L² + w²

we obtain :

L = 14 - w           (1)

100 = L² + w²    (2)

if we substitute L by 14 - w in equation (2) we get:

100 = (14 - w)² + w² ⇔ w² - 14w + 98 = 0

solve the quadratic equation and you’ll get:

w = 6 or w = 8

now back to equation (1)

L = 14 - w = 14 - 6 = 8

then w = 6 and L = 8

:)

don't know what that says sorry i can't you

step-by-step explanation:

idk what it says

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).