Advertisements
Advertisements
प्रश्न
Complete the hexagonal and star shaped rangolies (see the given figures) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?
Advertisements
उत्तर
It can be observed that hexagonal-shaped rangoli has 6 equilateral triangles in it.
`"Area of "ΔOAB = sqrt3/4"(side)"^2`
`= sqrt3/4(5)^2`
`= sqrt3/4(25)`
`= (25sqrt3)/4cm^2`
`"Area of hexagonal-shaped rangoli "=6xx(25sqrt3)/4=(75sqrt3)/2cm^2`
`"Area of equilateral triangle having its side as 1cm "=sqrt3/4(1)^2=sqrt3/4cm^2`
`"Number of equilateral triangles of 1 cm side that can be filled in this hexagonal-shaped rangoli "=((75sqrt3)/2)/(sqrt3/4)=150`
Star-shaped rangoli has 12 equilateral triangles of side 5 cm in it.
`"Area of star-shaped rangoli "=12xxsqrt3/4xx(5)^2=75sqrt3`
`"Number of equilateral triangles of 1 cm side that can be filled in this star-shaped rangoli "=(75sqrt3)/(sqrt3/4)=300`
Therefore, star-shaped rangoli has more equilateral triangles in it.
संबंधित प्रश्न
Show that in a right angled triangle, the hypotenuse is the longest side.
AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see the given figure). Show that ∠A > ∠C and ∠B > ∠D.
From the following figure, prove that: AB > CD.
D is a point in side BC of triangle ABC. If AD > AC, show that AB > AC.
In ΔABC, the exterior ∠PBC > exterior ∠QCB. Prove that AB > AC.
In ΔPQR, PR > PQ and T is a point on PR such that PT = PQ. Prove that QR > TR.
In the given figure, ∠QPR = 50° and ∠PQR = 60°. Show that: SN < SR
In ΔABC, BC produced to D, such that, AC = CD; ∠BAD = 125° and ∠ACD = 105°. Show that BC > CD.
In ΔPQR, PS ⊥ QR ; prove that: PQ > QS and PQ > PS
In ΔPQR, PS ⊥ QR ; prove that: PQ + PR > QR and PQ + QR >2PS.
