Find all possible values of x in the similar triangles pqr stu

1 answer:

5 0

If triangles PQR and STU are similar then PQ corresponds to ST and PR corresponds to SU. Therefore, PQ/ST=PR/SU
Considering that, PQ= 7-x, ST= 13-x, PR= x²+5 and SU= x² +20
therefore, (7-x)/(13-x)= (x²+5)/(x²+20)
cross multiplying,
7x² +140-x³+20x =13x²+65-x³-5x
combining the like terms,
6x² +15x -75=0
solving for x,
x = 5/2 or -5

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timama [110]

Answer:

The volume of the irregular figure would be 144 $cm^3$ .

Step-by-step explanation:

If you wish to make the process of calculating the volume easier, you can picture the irregular figure as two rectangular prisms: the large one on the bottom, and the smaller one appearing to protrude from the prism below it. Using this method, you only need to find the volumes of the two rectangular prisms and add the values together to get the volume for the irregular figure. The formula used to find the volume of a rectangular prism is $l*w*h$ , where $l$ , $w$ , and $h$ , represents the length, width, and height of the rectangular prism respectively. Using the formula above, the volume of the larger rectangular prism would be 12 * 3 * 3 = 12 * 9 = 108 $cm^3$ , and the volume of the smaller rectangular prism would be 4 * 3 * 3 = 12 * 3 = 36 $cm^3$ . So the volume of the entire irregular figure would be 108 + 36 = 144 $cm^3$ .