the length of a rectangle is 1 1/8 cm longer than the width. The perimiter of the rectangle is 13 1/4 cm. What are the width and length?

Length = 3 7/8cm

Width  = 2 3/4 cm

Step-by-step explanation

Let the length of the rectangle by L

Let the width be W

If the length of a rectangle is 1 1/8 cm longer than the width, then;

L = W + 1 1/8

L = W +9/8

perimeter of the  rectangle = 2(L+W)

perimeter of the  rectangle = 2(W + 9/8 + W)

13 1/4 = 2(2W + 9/8)

53/4 = 4W + 9/4

4W = 53/4 - 9/4

4W = 44/4

4W = 11

W = 11/4

Hence the width of the rectangle is 11/4 or 2 3/4 cm

Recall that L = W + 9/8

L = 11/4 + 9/8

L = (2(11) + 9)/8

L = 31/8

L = 3 7/8cm

hence the length is 3 7/8 cm

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.