Answer:
area of triangle =1/2×perpendicular×base
35m²×2=(g-11)(g-8)
70=g(g-8)-11(g-8)
70=g²-8g-11g+88
70=g²-19g+88
0=g²-19g+88-70
0=g²-19g+18
g²-18g-g+18=0
g(g-18)-1(g-18)=0
(g-18)(g-1)=0
either
g=18
or
g=1
Step-by-step explanation:
base=18-8=10m
perpendicular=18-11=7m
The dimensions of the polygon in the shape of right angle triangle is 10 m by 7 m.
The area of the right angle triangle is the space occupied by it on the two-dimensional plane.
The area of the right angle triangle is half of the product of base and height.
[tex]A=\dfrac{1}{2}bh[/tex]
Here, (b) is the base of the triangle and (h) is the height.
The area of the polygon is 35 m². The height of the triangle is (g - 11) m and base is (g - 8) m. Thus, using the above formula,
[tex]A=\dfrac{1}{2}bh\\35=\dfrac{1}{2}(g-11)(g-8)\\70=g^2-8g-11g+88\\0=g^2-19g+18\\[/tex]
On factorizing above equation,
[tex]0=(g-18)(g-1)\\g=18,1[/tex]
Taking the bigger root, the height of the polygon is,
[tex]h=g-11)\\h=18-11\\h=7\rm\;m[/tex]
The base of the polygon is,
[tex]b=(g-8)\\b=18-8\\b=10\rm\;m[/tex]
Hence, the dimensions of the polygon in the shape of right angle triangle is 10 m by 7 m.
Learn more about the right angle triangle here;
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