Geometry question I need help on

Question

Given BOAT is a rhombus with BO = 4x – 7, TO = 30, and perimeter of 9x + 14. Determine BA.

By the way, BA is diagonal and TO is diagonal.

Answer 1

draw a diagram

BO=4x-7

diagonal TO=30

perimeter=9x+14

first find x

perimeter=4 times any side

4(4x-7)=9x+14

16x-28=9x+14

7x=42

x=6

BO=4*6-7

BO=24-7

BO=17

the diagonals of a rhombus are perpendicular to each and also bisect each other

call the intersection of BA and TO point D

you now have a right triangle BDO where angle BDO is 90°

BO is the hypotenuse and is equal to 17

DO is half of 30 so DO equals 15

now find BD, which is half of BA using the Pythagorean Theorem

17^2=15^2+BD^2

289=225+BD^2

BD^2=289-225

BD^2=64

take the square root of both sides

BD=√64

BD=8

BD=DA=8

BA=BD+DA

BA=8+8=16 answer

Answer 2

Please see the video.

Answer 3

Hi Shelly,

The four consecutive sides of a rhombus are congruent. We are given one side measurement and the perimeter.

so 4 ( 4 x -7 ) = 9 x +14

solve for x and then substitute to determine side length. The diagonals bisect each other and are perpendicular. This is a very important property of a rhombus.

Set up your equation for a right triangle given the length of the side and that TO is bisected. Now solve the equation and then double it to find the length of BA.

I hope this helps.